On applying Lie-group symmetry analysis to the functional Hopf-Burgers equation in physical space

The recent systematic study by Janocha et al. [Symmetry 2015, 7, 1536-1566] to determine all possible Lie-point symmetries for the functional Hopf-Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf-Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach.